What is the next term of the geometric sequence? $\dfrac{40}{27},\dfrac{20}{9},\dfrac{10}{3},$
In a geometric sequence there's a constant ratio between subsequent terms. Let's find that ratio, and use it to find which term should come after the last one that is given, which is $\dfrac{10}{3}$. Each term is ${\dfrac32}$ times the term before it. ${\times \dfrac32\,\curvearrowright}$ ${\times \dfrac32\,\curvearrowright}$ $\dfrac{40}{27},$ $\dfrac{20}{9},$ $\dfrac{10}{3}$ So the next term is $\dfrac{10}{3}\cdot{\dfrac32}=5$. The missing term is $5$.